MinT - Best Known (101, 101+154, s)-Nets in Base 4

Best Known (101, 101+154, s)-Nets in Base 4

(101, 101+154, 104)-Net over F₄ — Constructive and digital

Digital (101, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(101, 101+154, 144)-Net over F₄ — Digital

Digital (101, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(101, 101+154, 906)-Net in Base 4 — Upper bound on s

There is no (101, 255, 907)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3370 054261 403139 847461 066803 435070 401946 800746 575986 101708 313005 066763 018703 501685 893137 599022 054383 940353 978193 304775 484735 979685 974369 268960 143953 412160 > 4²⁵⁵ [i]